Convex or concave hull, depending on quad or non quad, why this behavior?
I showed a similar example to your first before. The quad is always cut from vert 0 to vert 3, while n-gons are triangulated using a better algorithm, possibly because the possibility of concave faces is more likely.

You will also find that an n-gon is triangulated dynamically as you alter it.



I expect the tri/quad drawing code was left alone when n-gon support was added. Maybe it could be suggested that the work being done for 2.80 could include the use of same drawing algorithm for all faces.